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Multiple equilibria and indifference-threshold points in a rational addiction model

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  • Jonathan Caulkins
  • Gustav Feichtinger
  • Richard Hartl
  • Peter Kort
  • Andreas Novak
  • Andrea Seidl

Abstract

Becker and Murphy (J Polit Econ 96(4):675–700, 1988 ) have established the existence of unstable steady states leading to threshold behavior for optimal consumption rates in intertemporal rational addiction models. In the present paper a simple linear-quadratic optimal control model is used to illustrate how their approach fits into the framework of multiple equilibria and indifference-threshold points. By changing the degree of addiction and the level of harmfulness we obtain a variety of behavioral patterns. In particular we show that when the good is harmful as well as very addictive, an indifference-threshold point, also known in the literature as a Skiba point, separates patterns converging to either zero or maximal consumption, where the latter occurs in the case of a high level of past consumption. This implicitly shows that an individual needs to be aware in time of these characteristics of the good. Otherwise, he/she may start consuming so much that in the end he/she is totally addicted. Copyright Springer-Verlag 2013

Suggested Citation

  • Jonathan Caulkins & Gustav Feichtinger & Richard Hartl & Peter Kort & Andreas Novak & Andrea Seidl, 2013. "Multiple equilibria and indifference-threshold points in a rational addiction model," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 21(3), pages 507-522, September.
    • Handle: RePEc:spr:cejnor:v:21:y:2013:i:3:p:507-522
    DOI: 10.1007/s10100-012-0260-9
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    References listed on IDEAS

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    1. Dieter Grass & Jonathan P. Caulkins & Gustav Feichtinger & Gernot Tragler & Doris A. Behrens, 2008. "Optimal Control of Nonlinear Processes," Springer Books, Springer, number 978-3-540-77647-5, April.
    2. Wagener, F. O. O., 2003. "Skiba points and heteroclinic bifurcations, with applications to the shallow lake system," Journal of Economic Dynamics and Control, Elsevier, vol. 27(9), pages 1533-1561, July.
    3. Dechert, W. Davis, 1983. "Increasing returns to scale and the reverse flexible accelerator," Economics Letters, Elsevier, vol. 13(1), pages 69-75.
    4. Wirl, Franz & Feichtinger, Gustav, 2005. "History dependence in concave economies," Journal of Economic Behavior & Organization, Elsevier, vol. 57(4), pages 390-407, August.
    5. Orphanides, Athanasios & Zervos, David, 1994. "Optimal consumption dynamics with non-concave habit-forming utility," Economics Letters, Elsevier, vol. 44(1-2), pages 67-72.
    6. repec:bla:kyklos:v:45:y:1992:i:3:p:327-45 is not listed on IDEAS
    7. R. F. Hartl & P. M. Kort & G. Feichtinger & F. Wirl, 2004. "Multiple Equilibria and Thresholds Due to Relative Investment Costs," Journal of Optimization Theory and Applications, Springer, vol. 123(1), pages 49-82, October.
    8. Norman Brown & Paolo Vanini, 2003. "On Habits and Addictions," Journal of Institutional and Theoretical Economics (JITE), Mohr Siebeck, Tübingen, vol. 159(4), pages 603-626, December.
    9. Brock, W A & Dechert, W D, 1985. "Dynamic Ramsey Pricing," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 26(3), pages 569-591, October.
    10. Gary S. Becker, 1992. "Habits, Addictions, and Traditions," Kyklos, Wiley Blackwell, vol. 45(3), pages 327-345, August.
    11. Orphanides, Athanasios & Zervos, David, 1995. "Rational Addiction with Learning and Regret," Journal of Political Economy, University of Chicago Press, vol. 103(4), pages 739-758, August.
    12. Stigler, George J & Becker, Gary S, 1977. "De Gustibus Non Est Disputandum," American Economic Review, American Economic Association, vol. 67(2), pages 76-90, March.
    13. Lucas, Robert Jr., 1988. "On the mechanics of economic development," Journal of Monetary Economics, Elsevier, vol. 22(1), pages 3-42, July.
    14. W. Davis Dechert & Kazuo Nishimura, 2012. "A Complete Characterization of Optimal Growth Paths in an Aggregated Model with a Non-Concave Production Function," Springer Books, in: John Stachurski & Alain Venditti & Makoto Yano (ed.), Nonlinear Dynamics in Equilibrium Models, edition 127, chapter 0, pages 237-257, Springer.
    15. Skiba, A K, 1978. "Optimal Growth with a Convex-Concave Production Function," Econometrica, Econometric Society, vol. 46(3), pages 527-539, May.
    16. Dockner, Engelbert J & Feichtinger, Gustav, 1993. "Cyclical Consumption Patterns and Rational Addiction," American Economic Review, American Economic Association, vol. 83(1), pages 256-263, March.
    17. Auld, M. Christopher & Grootendorst, Paul, 2004. "An empirical analysis of milk addiction," Journal of Health Economics, Elsevier, vol. 23(6), pages 1117-1133, November.
    18. David Cass, 1965. "Optimum Growth in an Aggregative Model of Capital Accumulation," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 32(3), pages 233-240.
    19. Iannaccone, Laurence R., 1986. "Addiction and satiation," Economics Letters, Elsevier, vol. 21(1), pages 95-99.
    20. Gavrila, C. & Feichtinger, G. & Tragler, G. & Hartl, R.F. & Kort, P.M., 2005. "History-dependence in a rational addiction model," Mathematical Social Sciences, Elsevier, vol. 49(3), pages 273-293, May.
    21. Harl E. Ryder & Geoffrey M. Heal, 1973. "Optimal Growth with Intertemporally Dependent Preferences," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 40(1), pages 1-31.
    22. Orphanides, Athanasios & Zervos, David, 1998. "Myopia and Addictive Behaviour," Economic Journal, Royal Economic Society, vol. 108(446), pages 75-91, January.
    23. Forster, Bruce A., 1975. "Optimal pollution control with a nonconstant exponential rate of decay," Journal of Environmental Economics and Management, Elsevier, vol. 2(1), pages 1-6, September.
    24. Becker, Gary S & Murphy, Kevin M, 1988. "A Theory of Rational Addiction," Journal of Political Economy, University of Chicago Press, vol. 96(4), pages 675-700, August.
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    1. Caulkins, Jonathan P. & Feichtinger, Gustav & Grass, Dieter & Hartl, Richard F. & Kort, Peter M. & Seidl, Andrea, 2015. "Skiba points in free end-time problems," Journal of Economic Dynamics and Control, Elsevier, vol. 51(C), pages 404-419.

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